Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and
cannot be solved analytically. Integrable systems lie on the other extreme. They possess …

In this work, we constructed the multi-soliton solutions to the Ward equation with the help of
the generalized Darboux transformation method. Importantly, we obtained the determinant …

The Ward equation, also called the modified 2+ 1 chiral model, is obtained by a dimension
reduction and a gauge fixing from the self-dual Yang-Mills field equation on R2, 2. It has a …

The space-time monopole equation is obtained from a dimension reduction of the anti-self
dual Yang-Mills equation on $\R^{2, 2} $. A family of Ward equations is obtained by gauge …

Let $(M, g) $ be a closed oriented negatively curved surface. A unitary connection on a
Hermitian vector bundle over $ M $ is said to be transparent if its parallel transport along the …

The usual dispersionless limit of the KP hierarchy does not work in the case where the
dependent variable has values in a noncommutative (eg matrix) algebra. Passing over to the …

In the noncommutative (Moyal) plane, we relate exact U (1) sigma-model solitons to generic
scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space Bbb C k/S k …

We generalize the results of [J. Villarroel, The inverse problem for Ward's system, Stud. Appl.
Math. 83 (1990) 211–222; AS Fokas, TA Ioannidou, The inverse spectral theory for the Ward …

We consider a class of time-dependent finite energy multi-soliton solutions of the U (N)
integrable chiral model in (2+ 1) dimensions. The corresponding extended solutions of the …

We use the compactified twistor correspondence for the (2+ 1)-dimensional integrable chiral
model to prove a conjecture of Ward. In particular, we construct the correspondence space …